Urban rail transit network train application and crew plan collaborative optimization method

Abstract

The invention relates to an urban rail transit network train application and crew plan collaborative optimization method. On the basis of a space-time network model, a train application and crew planning space-time network is constructed, and a branch-pricing-cutting algorithm framework is adopted to form the collaborative optimization method. According to the invention, the problems of too small crew plan adjustment space and multi-time feedback adjustment of the train application plan caused by the existing staged programming of the train application and crew plan are solved. Besides, according to the branch-pricing-cutting algorithm method based on the space-time network model provided by the invention, an accurate optimal solution can be solved and a convergence curve of upper and lower boundaries can be given within the calculation time shorter than that of integer programming solution software. The method provided by the invention can be popularized to more traffic space-time path coupling optimization problems, and redundant transportation capacity generated by respective compilation of different plans is fully excavated. The method is of great significance for improving the current rail transit network operation efficiency, the passenger service level, cost reduction and efficiency improvement of operation enterprises and the like.

Description

Technical Field

[0001] The present invention relates to the technical field of urban rail transit operation management, and in particular to a method for collaboratively optimizing train operation and crew planning in an urban rail transit network. Background Art

[0002] Urban rail transit systems have the advantages of high safety, fast and convenient, low environmental pollution, high punctuality and good comfort. They have developed rapidly in many large cities and gradually become the backbone of urban commuting. Generally speaking, the management of urban rail transit network systems involves a complex operation planning process, such as Figure 1 As shown in the figure, it includes the comprehensive coordination and compilation of train operation plans, train operation diagrams, train turnover plans, train formation plans and crew plans from the tactical level to the operational level. Under the networked urban rail train operation mode, the train can flexibly select the operation plan according to the passenger flow demand on the urban rail network, and then generate the operation route and stop plan.

[0003] The compilation of train operation diagram is the core issue at the tactical level in the operation and management of urban rail transit. It usually refers to the departure and arrival time of trains at each station according to the train operation plan. Based on the given train operation diagram, the train turnover plan is compiled to allocate corresponding car bodies for different train operation lines, and then the turnover path of each car body in the planned time domain is obtained. In order to fully meet the different travel frequency requirements of different physical sections on urban rail transit lines in different time periods, a flexible train marshaling mode is used in the train marshaling plan, in which two fixed short marshaling trains (6-carriage or 8-carriage marshaling) can be further marshaled to form a long marshaling train with larger passenger capacity (12-carriage or 16-carriage marshaling). At the same time, the long marshaling train can also be decomposed into two short marshaling trains as needed, which helps to meet the passenger needs of different physical sections during peak / valley periods by flexibly adjusting the train marshaling and reduce resource waste. On the basis of the car body utilization plan and the train marshaling plan, the crew plan is further marshaled to ensure that a crew is assigned to each train trip.

[0004] By analyzing the existing urban rail transit operation organization process and related literature, the existing methods usually compile train operation diagrams, vehicle bottom operation plans, train formation plans and crew plans in sequence and independently. The obtained operation plans are difficult to ensure the coordination between different plans, which is not conducive to the rational allocation of resources. At the same time, the phased compilation of train operation and crew plans leads to too little adjustment space for the latter, which restricts the improvement of transportation capacity and cost reduction and efficiency improvement. Summary of the invention

[0005] In view of the defects existing in the prior art, the purpose of the present invention is to provide a method for collaborative optimization of train operation and crew planning in an urban rail transit network. The method describes the process of train units entering and exiting the yard, marshaling, disassembling and turning back, as well as the crew's duty, dining and resting processes based on a spatiotemporal network, and designs a solution algorithm based on branch-pricing-cutting. From the perspective of system optimization, the method collaboratively optimizes the train operation diagram, vehicle turnover plan, train marshaling plan, and crew plan, improves the incoordination problem in operational management caused by the independent preparation of train operation and crew plans, and provides decision support for scientific operation organization.

[0006] In order to achieve the above purpose, the technical solution adopted by the present invention is:

[0007] A method for collaborative optimization of train operation and crew planning in an urban rail transit network, characterized in that it comprises the following steps:

[0008] Step 1: Based on the discrete space-time network, describe the process of train units entering and leaving the yard, marshaling, disassembling and turning back, as well as the crew's duty, dining and resting processes;

[0009] Step 2: Construct train operation organization constraints and crew scheduling constraints;

[0010] The train operation organization constraints include: train operation plan selection constraints, trip departure time constraints, train safety interval constraints, minimum trip frequency constraints, trip coverage constraints, train unit return constraints, and train connection time constraints;

[0011] Crew scheduling constraints include: crew task allocation constraints, crew task flow balance constraints, crew meal / rest task quantity balance constraints, crew on-duty and off-duty balance constraints, task connection time constraints, crew meal / rest frequency constraints, crew meal / rest time window constraints, train itinerary and crew task coupling constraints, and crew quantity constraints;

[0012] Step 3: Based on the train operation organization constraints and crew scheduling constraints described in step 2, a collaborative optimization model is constructed with the minimum total train operation cost and crew scheduling cost as the objective function;

[0013] The total train operation cost includes the fixed cost of train operation plan, fixed cost of trip and trip connection cost;

[0014] The crew scheduling cost includes the fixed cost of crew number;

[0015] Step 4: Based on the collaborative optimization model of train operation and crew planning constructed in step 3, reconstruct an equivalent collaborative optimization model based on train and crew paths;

[0016] Step 5: Construct the Benders main problem and Benders sub-problem for the equivalent collaborative optimization model based on the train and crew paths obtained in step 4;

[0017] Step 6: For the Benders main problem and Benders subproblem obtained in step 5, construct pricing subproblems respectively, and design a branch-price-cut algorithm to solve them until a feasible and better collaborative optimization solution is obtained.

[0018] Based on the above scheme, step 1 specifically includes:

[0019] For the train operation organization process, according to the accuracy requirements, the train planning time domain is discretized into a set of timestamps to form a timestamp set;

[0020] According to the discrete timestamp set, all physical nodes in the urban rail transit network are expanded in time and space; the physical nodes after time and space expansion include the time and space nodes of the station, the starting point of the yard and the end point of the yard;

[0021] Based on the above-mentioned space-time node set, a corresponding space-time arc set is constructed; specifically, it includes train travel arcs, entry / exit yard arcs, and connection arcs;

[0022] For the crew's duty process, a crew dining task set is constructed to describe the crew's dining behavior; a crew rest task set is constructed to describe the crew's rest behavior.

[0023] Based on the above scheme, the train operation organization constraints described in step 2 specifically include:

[0024] The train operation plan selection constraint condition is: for each train unit, only one suitable train operation plan can be selected from its corresponding train operation plan alternative set, as shown in formula (1):

[0025]

[0026] In the above formula, set K represents the train unit set, set L k represents the set of alternative train operation plans corresponding to train unit k; decision variable u k,l Indicates whether the train operation plan l is selected by the train unit k. If the train operation plan l is selected by the train unit k, then u k,l =1, otherwise u k,l = 0; the "train unit k" field is an index for retrieving train unit k, and the "train operation plan l" field is an index for retrieving train operation plan l;

[0027] The trip departure time constraint condition is used to ensure that each trip in the train operation plan selected by the train unit departs within its specified time window, as shown in formula (2):

[0028]

[0029] In the above formula, set K represents the train unit set, set L k represents the set of train operation alternatives corresponding to train unit k, set R l T represents the set of itinerary tasks corresponding to the operation plan l; set T r represents the departure timestamp set corresponding to the trip task r; the decision variable x r,t represents whether the trip task r departs at timestamp t. If the trip task r departs at timestamp t, then x r,t =1, otherwise x r,t =0; decision variable u k,l Indicates whether the train operation plan l is selected by the train unit k. If the train operation plan l is selected by the train unit k, then u k,l =1, otherwise u k,l = 0; the "train unit k" field is an index for retrieving train unit k, the "train operation plan l" field is an index for retrieving train operation plan l; the "task r" field is an index for retrieving task r; the "timestamp t" field is an index for retrieving timestamp t;

[0030] The train safety interval constraint is used to ensure that there is no conflict between the trips, so as to ensure the safe operation of the train, as shown in formula (3):

[0031]

[0032] In the above formula, set T represents the total planning timestamp set, set T r and T r’ represents the departure timestamp set corresponding to the itinerary tasks r and r', and the set V represents the set of potential conflicting itineraries; the parameters represents the minimum safe interval between potentially conflicting tasks r and r'; decision variable x r,t represents whether the trip task r departs at timestamp t. If the trip task r departs at timestamp t, then x r,t =1, otherwise x r,t = 0; the "task r" field is the index for retrieving task r, the "task r'" field is the index for retrieving task r', the "timestamp t" field is the index for retrieving timestamp t, the "timestamp t'" field is the index for retrieving timestamp t, and the tuple (r, r') represents a potential conflicting itinerary task pair;

[0033] The potential conflicting trip set V is determined by formula (4), that is, for trip tasks r and r', if the physical intervals of the operation are the same and the departure time windows overlap, it is defined as a potential conflicting trip task pair (r, r') and is put into the set V;

[0034]

[0035] In the above formula, the set T r and T r’ represents the departure timestamp set corresponding to the itinerary tasks r and r', the set V represents the set of potential conflicting itineraries, and the set R T represents a set of travel tasks; parameters a(r) and a(r') represent the running intervals corresponding to travel tasks r and r'; the "task r" field is the index used to retrieve travel task r, the "task r'" field is the index used to retrieve task r', the "timestamp t" field is the index used to retrieve timestamp t, and the "timestamp t'" field is the index used to retrieve timestamp t. The tuple (r, r') represents a potentially conflicting travel task pair;

[0036] The minimum trip frequency constraint condition is that for each physical operation interval and a given scenario, according to the spatiotemporal passenger flow demand information, the number of trips departing within the time window of a given scenario must not be less than the minimum number of trips, as shown in formula (5):

[0037]

[0038] In the above formula, set A represents the set of physical intervals; set S a represents the set of travel frequency requirement scenarios for physical interval a; set T s represents the travel frequency requirement timestamp set corresponding to scenario s; set T r Represents the departure timestamp set corresponding to the trip task r; set R T Represents a set of itinerary tasks; parameters Represents the minimum number of trips departing from the timestamp set corresponding to scenario s; parameter δ r,a Indicates whether the trip task r passes through the physical interval a. If the trip task r passes through interval a, then δ r,a =1, otherwise δ r,a =0; decision variable x r,t represents whether the trip task r departs at timestamp t. If the trip task r departs at timestamp t, then x r,t =1, otherwise x r,t = 0; the "interval a" field is an index for retrieving the physical interval a, the "scene s" field is an index for retrieving the scene s, the "task r" field is an index for retrieving the trip r, and the "timestamp t" field is an index for retrieving the timestamp t.

[0039] The trip coverage constraint condition is based on the flexible marshaling train operation condition requirements. For each physical operation interval and timestamp, the number of covered train units shall not exceed the train marshaling upper limit, as shown in formula (6):

[0040]

[0041] In the above formula, set A represents the physical interval set, set T represents the total planning timestamp set, and set R T represents the set of itinerary tasks; parameter δ r,a Indicates whether the trip task r passes through the physical interval a. If the trip task r passes through interval a, then δ r,a =1, otherwise δ r,a =0; parameter represents the maximum number of train formations in interval a at any time; decision variable x r,t represents whether the trip task r departs at timestamp t. If the trip task r departs at timestamp t, then x r,t =1, otherwise x r,t = 0; the "interval a" field is an index for retrieving physical interval a, the "task r" field is an index for retrieving task r, and the "timestamp t" field is an index for retrieving timestamp t.

[0042] The train unit reversal constraint condition is used to ensure that the connection time of the train unit when connecting two adjacent trips shall not be less than the minimum reversal time and shall not exceed the maximum reversal time, as shown in formulas (7) and (8):

[0043]

[0044] In the above two equations, set K represents the train unit set, and set L k represents the set of train operation alternatives corresponding to train unit k, set R l T represents the set of itinerary tasks corresponding to the operation plan l; set T r and T σ(r) represents the departure timestamp set corresponding to the trip task r and σ(r); parameter σ(r) represents the only previous trip task of the trip task r, parameter r0(l) represents the first trip task of the train operation plan l, and parameter represents the travel time of the trip task σ(r); parameter represents the minimum connection time between the trip task σ(r) and the trip task r; parameter represents the maximum connection time between the trip task σ(r) and the trip task r; the decision variable x r,t represents whether the trip task r departs at timestamp t. If the trip task r departs at timestamp t, then x r,t =1, otherwise x r,t=0; decision variable u k,l Indicates whether the train operation plan l is selected by the train unit k. If the train operation plan l is selected by the train unit k, then u k,l =1, otherwise u k,l = 0; the "train unit k" field is an index for retrieving train unit k, the "running plan l" field is an index for retrieving running plan l, the "task r" field is an index for retrieving task r, and the "timestamp t" field is an index for retrieving timestamp t.

[0045] The train connection time constraint is used to calculate the actual return time of the train unit between two adjacent trips, as shown in formula (9):

[0046]

[0047] In the above formula, set K represents the train unit set, set L k represents the set of train operation alternatives corresponding to train unit k, set R l T represents the set of itinerary tasks corresponding to the operation plan l; set T r and T σ(r) represents the departure timestamp set corresponding to the trip task r and σ(r); parameter σ(r) represents the only previous trip task of the trip task r, parameter r0(l) represents the first trip task of the train operation plan l, and parameter represents the travel time of the trip task σ(r); the decision variable x r,t represents whether the trip task r departs at timestamp t. If the trip task r departs at timestamp t, then x r,t =1, otherwise x r,t =0; decision variable v k,σ(r),r represents the actual connection time between the train unit k connecting the trip tasks σ(r) and r; the "train unit k" field is an index for retrieving the train unit k, the "running plan l" is an index for retrieving the running plan l, the "task r" field is an index for retrieving the task r, and the "timestamp t" field is an index for retrieving the timestamp t.

[0048] Based on the above scheme, the crew scheduling constraints described in step 2 specifically include:

[0049] The crew task allocation constraint condition is that for each crew member, at most one trip or meal / rest task starts, as shown in formula (10):

[0050]

[0051] In the above formula, set C represents the crew set; set R TRepresents the set of itinerary tasks, set R c M represents the dining task set corresponding to crew member c, set R c R represents the rest task set corresponding to crew member c; decision variable z c,0,r Indicates whether the trip task r is connected to the virtual starting node. If the trip task r is connected to the virtual starting node, then z c,0,r =1, otherwise z c,0,r = 0; the "crew member c" field is an index for retrieving crew member c, and the "task r" field is an index for retrieving task r;

[0052] The flow balance constraint of the crew tasks is that for each crew member, any trip or meal / rest task needs to be connected to other tasks or start / end nodes, as shown in formula (11):

[0053]

[0054] In the above formula, set C represents the crew set; set R T Represents the set of itinerary tasks, set R c M represents the dining task set corresponding to crew member c, set R c R represents the set of rest tasks corresponding to crew member c; set R r T- Represents the set of previous consecutive trip tasks of trip task r, set R r T+ represents the set of next consecutive trip tasks of trip task r; decision variable z c,0,r Indicates whether the trip task r is connected to the virtual starting node. If the trip task r is connected to the virtual starting node, then z c,0,r =1, otherwise z c,0,r =0; decision variable z c,r’,r Indicates whether the trip task r is connected to another trip task r'. If the trip task r is connected to another trip task r', then z c,r’,r =1, otherwise z c,r’,r =0; decision variable z c,r,0 Indicates whether the trip task r is connected to the virtual destination node. If the trip task r is connected to the virtual destination node, then z c,r,0 =1; otherwise z c,r,0 =0; the "crew member c" field is an index for retrieving crew member c, the "task r" field is an index for retrieving task r, and the "task r'" field is an index for retrieving task r';

[0055] The balance constraint of the number of crew meal / rest tasks is that for each crew meal / rest task, there can only be two trip tasks as its next and previous successor tasks, as shown in formula (12):

[0056]

[0057] In the above formula, set C represents the crew set; set R c M represents the dining task set corresponding to crew member c, set R c R represents the rest task set corresponding to crew member c; set R r T- Represents the set of previous consecutive trip tasks of trip task r, set R r T+ represents the set of next consecutive trip tasks of trip task r; decision variable z c,0,r Indicates whether the trip task r is connected to the virtual starting node. If the trip task r is connected to the virtual starting node, then z c,0,r =1, otherwise z c,0,r =0; decision variable z c,r’,r Indicates whether the trip task r is connected to another trip task r'. If the trip task r is connected to another trip task r', then z c,r’,r =1, otherwise z c,r’,r =0; decision variable z c,r,0 Indicates whether the trip task r is connected to the virtual destination node. If the trip task r is connected to the virtual destination node, then z c,r,0 =1; otherwise z c,r,0 =0; the "crew member c" field is an index for retrieving crew member c, the "task r" field is an index for retrieving task r, and the "task r'" field is an index for retrieving task r';

[0058] The crew on-duty and off-duty balance constraint ensures that there is a first and last task for each crew member on duty, and that there is no first and last task for each crew member not on duty, as shown in formula (13):

[0059]

[0060] In the above formula, set C represents the crew set, set R T Represents the set of itinerary tasks, set R c M represents the dining task set corresponding to crew member c, set R c R represents the rest task set corresponding to crew member c; decision variable z c,0,rIndicates whether the trip task r is connected to the virtual starting node. If the trip task r is connected to the virtual starting node, then z c,0,r =1, otherwise z c,0,r =0; decision variable z c,r,0 Indicates whether the trip task r is connected to the virtual destination node. If the trip task r is connected to the virtual destination node, then z c,r,0 =1; otherwise z c,r,0 = 0; the "crew member c" field is an index for retrieving crew member c, and the "task r" field is an index for retrieving task r;

[0061] The task connection time constraint is used to ensure that the connection time between two consecutive tasks performed by the crew members meets the specified requirements, as shown in formulas (14) and (15):

[0062]

[0063] In the above two equations, set C represents the crew set, set R T Represents the set of itinerary tasks, set R c M represents the dining task set corresponding to crew member c, set R c R represents the rest task set corresponding to crew member c; set T r and T r’ Represents the departure timestamp set corresponding to the trip tasks r and r'; parameter and Respectively represent the minimum and maximum connection time between two consecutive tasks performed by the crew; parameter T r R represents the travel time of trip task r; the decision variable x r,t represents whether the trip task r departs at timestamp t. If the trip task r departs at timestamp t, then x r,t =1, otherwise x r,t =0; decision variable z c,r,r’ Indicates whether the trip task r' is connected to another trip task r. If the trip task r' is connected to another trip task r, then z c,r,r’ =1, otherwise z c,r,r’ = 0; the "crew member c" field is an index for retrieving crew member c, the "task r" field is an index for retrieving task r, the "task r'" field is an index for retrieving task r', and the "timestamp t" field is an index for retrieving timestamp t; parameter M r,r’ represents the maximum M value corresponding to r and r' in formula (14) and formula (15), which is determined by formula (16):

[0064]

[0065] In the above formula, set C represents the crew set, set R T Represents the set of itinerary tasks, set R c M represents the dining task set corresponding to crew member c, set R c R represents the rest task set corresponding to crew member c; parameter T r and Represent the earliest start time and the latest start time of the trip task r respectively; parameter T r R represents the travel time of trip task r; parameter Represents the maximum duration between two consecutive tasks performed by a crew member; the "Crew member c" field is an index for retrieving crew member c, the "Task r" field is an index for retrieving task r, and the "Task r'" field is an index for retrieving task r';

[0066] The crew meal / rest frequency constraint ensures that every crew member on duty must perform the corresponding meal / rest task, as shown in formula (17):

[0067]

[0068] In the above formula, set C represents the crew set, set R T Represents the set of itinerary tasks, set R c M represents the dining task set corresponding to crew member c, set R c R represents the rest task set corresponding to crew member c, set R r T- represents the set of previous consecutive trip tasks of trip task r; decision variable z c,0,r Indicates whether the trip task r is connected to the virtual starting node. If the trip task r is connected to the virtual starting node, then z c,0,r =1, otherwise z c,0,r =0; decision variable z c,r’,r Indicates whether the trip task r is connected to another trip task r'. If the trip task r is connected to another trip task r', then z c,r’,r =1, otherwise z c,r’,r =0; the "crew member c" field is an index for retrieving crew member c, the "task r" field is an index for retrieving task r, and the "task r'" field is an index for retrieving task r';

[0069] The crew meal / rest time window constraint ensures that each meal / rest task must be executed within the specified time window, as shown in formula (18):

[0070]

[0071] Among them, set C represents the crew set, set R T Represents the set of itinerary tasks, set R c M represents the dining task set corresponding to crew member c, set R c R represents the rest task set corresponding to crew member c, set T r represents the departure timestamp set corresponding to the trip task r; the decision variable x r,t represents whether the trip task r departs at timestamp t. If the trip task r departs at timestamp t, then x r,t =1, otherwise x r,t =0; decision variable z c,0,r Indicates whether the trip task r is connected to the virtual starting node. If the trip task r is connected to the virtual starting node, then z c,0,r =1, otherwise z c,0,r =0; decision variable z c,r’,r Indicates whether the trip task r is connected to another trip task r'. If the trip task r is connected to another trip task r', then z c,r’,r =1, otherwise z c,r’,r =0; the "crew member c" field is an index for retrieving crew member c, the "task r" field is an index for retrieving task r, the "task r'" field is an index for retrieving task r', and the "timestamp t" field is an index for retrieving timestamp t;

[0072] The train itinerary and crew task coupling constraint, for any itinerary, should ensure that at least one crew member is assigned to the itinerary, as shown in formula (19):

[0073]

[0074] Among them, set C represents the crew set, set R T Represents the set of itinerary tasks, set R c M represents the dining task set corresponding to crew member c, set R c R represents the rest task set corresponding to crew member c, set T r Represents the departure timestamp set corresponding to the trip task r, set R r T- represents the set of previous consecutive trip tasks of trip task r; decision variable xr,t represents whether the trip task r departs at timestamp t. If the trip task r departs at timestamp t, then x r,t =1, otherwise x r,t =0; decision variable z c,0,r Indicates whether the trip task r is connected to the virtual starting node. If the trip task r is connected to the virtual starting node, then z c,0,r =1, otherwise z c,0,r =0; decision variable z c,r’,r Indicates whether the trip task r is connected to another trip task r'. If the trip task r is connected to another trip task r', then z c,r’,r =1, otherwise z c,r’,r =0; the "crew member c" field is an index for retrieving crew member c, the "task r" field is an index for retrieving task r, the "task r'" field is an index for retrieving task r', and the "timestamp t" field is an index for retrieving timestamp t;

[0075] The crew number constraint is used to calculate the number of crew members actually used for work by each crew group, as shown in formula (20):

[0076]

[0077] Among them, set G represents the crew set, set C g represents the crew set corresponding to crew group g, set R T Represents the set of itinerary tasks, set R c M represents the dining task set corresponding to crew member c, set R c R represents the rest task set corresponding to crew member c; decision variable m g represents the number of crew members corresponding to crew group g; decision variable z c,0,r Indicates whether the trip task r is connected to the virtual starting node. If the trip task r is connected to the virtual starting node, then z c,0,r =1, otherwise z c,0,r =0; the "crew member c" field is an index for retrieving crew member c, the "crew group g" field is an index for retrieving crew group g, and the "task r" field is an index for retrieving task r.

[0078] Based on the above scheme, the objective function described in step 3 is to minimize the total train operating cost and crew scheduling cost, as shown in formula (21):

[0079]

[0080] The first item is the sum of the fixed costs of the train operation plan, the second item is the sum of the train travel costs, the third item is the sum of the train unit connection costs, and the fourth item is the sum of the crew costs; set K represents the train unit set, set L k represents the set of train operation alternatives corresponding to train unit k, set R l T represents the set of itinerary tasks corresponding to the operation plan l; set T r represents the departure timestamp set corresponding to the trip task r, and the set G represents the crew set; the optimization goal min is to minimize the total cost; the decision variable u k,l Indicates whether the train operation plan l is selected by the train unit k. If the train operation plan l is selected by the train unit k, then u k,l =1, otherwise u k,l =0; decision variable x r,t represents whether the trip task r departs at timestamp t. If the trip task r departs at timestamp t, then x r,t =1, otherwise x r,t =0; decision variable v k,σ(r),r represents the actual connection time between train unit k and the trip task σ(r) and r; the decision variable m g represents the number of crew members corresponding to crew group g; parameter c k,l 1 represents the fixed cost of train unit k choosing train operation plan l; parameter c r,t 2 represents the fixed cost of the trip task r starting at timestamp t; parameter c σ(r),r 3 represents the fixed cost per unit time of the trip task σ(r) and the trip task r; parameter c g 4 represents the fixed cost of arranging a crew member in crew group g, parameter σ(r) represents the only previous trip task of trip task r, parameter r0(l) represents the first trip task of train operation plan l; the "train unit k" field is the index used to retrieve train unit k, the "operation plan l" field is the index used to retrieve operation plan l, the "task r" field is the index used to retrieve task r, the "timestamp t" field is the index used to retrieve timestamp t, and the "crew group g" field is the index used to retrieve crew group g;

[0081] Based on the above scheme, the train operation and crew planning collaborative optimization model constructed in step 3 described in step 4 is reconstructed to obtain a collaborative optimization model based on train and crew paths, which specifically includes:

[0082] The collaborative optimization model based on the train and crew paths specifically includes train unit path selection constraints, train safety interval constraints based on the train path, minimum travel frequency constraints based on the train path, travel coverage constraints based on the train path, and coupling constraints between train units and crew based on the train path;

[0083] The train unit path selection constraint condition is that for each train unit, only one path can be selected from its feasible path set, as shown in formula (22):

[0084]

[0085] In the above formula, the set represents the set of feasible paths corresponding to train unit k, where set K represents the set of train units; decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p = 0; the "path p" field is an index for retrieving path p, and the "train unit k" field is an index for retrieving train unit k;

[0086] The train safety interval constraint condition based on the train path ensures that there is no conflict between the trips to ensure the safe operation of the train, as shown in formula (23):

[0087]

[0088] In the above formula, set T represents the total planning timestamp set, set V represents the potential conflicting itinerary set, and set P R Represents the set of feasible paths for the train unit; parameter Represents the minimum safe interval between potentially conflicting itinerary tasks r and r'; parameter α p,r,t represents whether path p includes the travel task r starting at timestamp t. If path p includes the travel task r starting at timestamp t, then α p,r,t =1, otherwise α p,r,t =0; decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p = 0; the "path p" field is an index for retrieving path p, the "task r" field is an index for retrieving task r, the "task r'" field is an index for retrieving task r', the "timestamp t" field is an index for retrieving timestamp t, the "timestamp t'" field is an index for retrieving timestamp t, and the tuple (r, r') represents a potential conflicting itinerary task pair;

[0089] The potential conflicting trip set V is determined by formula (4), that is, for trip tasks r and r', if the physical intervals of the operation are the same and the departure time windows overlap, it is defined as a potential conflicting trip task pair (r, r') and is put into the set V;

[0090]

[0091] In the above formula, the set T r and T r’ represents the departure timestamp set corresponding to the itinerary tasks r and r', the set V represents the set of potential conflicting itineraries, and the set R T represents a set of travel tasks; parameters a(r) and a(r') represent the running intervals corresponding to travel tasks r and r'; the "task r" field is the index used to retrieve travel task r, the "task r'" field is the index used to retrieve task r', the "timestamp t" field is the index used to retrieve timestamp t, and the "timestamp t'" field is the index used to retrieve timestamp t. The tuple (r, r') represents a potentially conflicting travel task pair;

[0092] The minimum trip frequency constraint condition based on the train path is that for each physical operation interval and a given scenario, according to the spatiotemporal passenger flow demand information, the number of trips departing within the time window of a given scenario shall not be less than the minimum number of trips, as shown in formula (25):

[0093]

[0094] In the above formula, set A represents the set of physical intervals; set S a represents the set of travel frequency requirement scenarios for physical interval a; set T s represents the travel frequency requirement timestamp set corresponding to scenario s, set P R represents the set of feasible paths for the train unit; parameter β p,a,t Indicates whether path p passes through physical interval a at timestamp t. If path p passes through physical interval a at timestamp t, then β p,a,t =1, otherwise β p,a,t =0; parameter Represents the minimum number of trips departing within the time window corresponding to scenario s; decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p = 0; the "path p" field is an index for retrieving path p, the "interval a" field is an index for retrieving physical interval a, the "scene s" field is an index for retrieving scene s, the "task r" field is an index for retrieving trip r, and the "timestamp t" field is an index for retrieving timestamp t;

[0095] The travel coverage constraint condition based on the train path is based on the flexible marshaling train operation condition requirements. For each physical operation interval and timestamp, the number of covered train units shall not exceed the train marshaling upper limit, as shown in formula (26):

[0096]

[0097] In the above formula, set A represents the physical interval set, set T represents the total planning timestamp set, and set P R represents the set of feasible paths for the train unit; parameter β p,a,t Indicates whether path p passes through physical interval a at timestamp t. If path p passes through physical interval a at timestamp t, then β p,a,t =1, otherwise β p,a,t =0; parameter represents the maximum number of train formations in interval a at any time; decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p =0; the "path p" field is an index for retrieving path p, the "interval a" field is an index for retrieving physical interval a, and the "timestamp t" field is an index for retrieving timestamp t;

[0098] The coupling constraint between the train unit and the crew based on the train path is that for each trip and any timestamp in its departure time range, if the trip departs, it should be guaranteed that a crew is assigned to the trip, as shown in formula (27):

[0099]

[0100] In the above formula, the set R T Represents the set of itinerary tasks, set T r represents the departure timestamp set corresponding to the trip task r, set P R represents the set of feasible paths for train units, set P C represents the set of feasible paths for crew members; parameter α p,r,t represents whether path p includes the travel task r starting at timestamp t. If path p includes the travel task r starting at timestamp t, then α p,r,t =1, otherwise α p,r,t =0; parameter γ p,r Indicates whether path p includes itinerary task r. If path p includes itinerary task r, then γ p,r =1, otherwise γ p,r =0; decision variable μ p Indicates whether path p is selected. If path p is selected, μ p =1, otherwise μ p=0; decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p = 0; the "path p" field is an index for retrieving path p, the "task r" field is an index for retrieving task r, and the "timestamp t" field is an index for retrieving timestamp t;

[0101] The objective function is to minimize the total train operating cost and crew scheduling cost, as shown in formula (28):

[0102]

[0103] In the above formula, the set P R represents the set of feasible paths for train units, set P C represents the set of feasible paths for crew members; parameter C p R represents the cost of the train unit path p, parameter C p C represents the cost of crew member path p; decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p =0; decision variable μ p Indicates whether path p is selected. If path p is selected, μ p =1, otherwise μ p =0; the "path p" field is an index for retrieving path p;

[0104] Based on the above scheme, the train operation and crew planning collaborative optimization model based on the spatiotemporal network described in step 5 constructs the Benders main problem and Benders sub-problems, which specifically include:

[0105] The Benders main problem specifically includes the Benders main problem objective function, the Benders main problem train unit path selection constraint, the Benders main problem train safety interval constraint, the Benders main problem minimum travel frequency constraint, the Benders main problem travel coverage constraint and the Benders optimal cut constraint;

[0106] The objective function of the Benders main problem includes the total train operating cost and the Benders optimal cut upper bound, as shown in formula (29):

[0107]

[0108] In the above formula, the set Represents the set of restricted feasible paths for train units; parameter C p R represents the cost of the train unit path p; the decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p =0; the decision variable η represents the upper limit of the Benders optimal cut; the optimization goal min is to minimize the total train operation cost and the upper limit of the Benders optimal cut; the "path p" field is the index used to retrieve the path p;

[0109] The Benders master problem train unit path selection constraint condition is that for each train unit, only one path can be selected from its restricted feasible path set, as shown in formula (30):

[0110]

[0111] In the above formula, the set represents the set of restricted feasible paths corresponding to train unit k, where set K represents the set of train units; decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p = 0; the "path p" field is an index for retrieving path p, and the "train unit k" field is an index for retrieving train unit k;

[0112] The Benders main problem train safety interval constraint condition ensures that there is no conflict between the trips to ensure the safe operation of the train, as shown in formula (31):

[0113]

[0114] In the above formula, set T represents the total planning timestamp set, set T r and T r’ represents the departure timestamp set corresponding to the itinerary tasks r and r', set V represents the set of potential conflicting itineraries, and set Represents the set of restricted feasible paths for train units; parameters Represents the minimum safe interval between potentially conflicting itinerary tasks r and r'; parameter α p,r,t represents whether path p includes the travel task r starting at timestamp t. If path p includes the travel task r starting at timestamp t, then α p,r,t =1, otherwise α p,r,t =0; decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p= 0; the "path p" field is an index for retrieving path p, the "task r" field is an index for retrieving task r, the "task r'" field is an index for retrieving task r', the "timestamp t" field is an index for retrieving timestamp t, the "timestamp t'" field is an index for retrieving timestamp t, and the tuple (r, r') represents a potential conflicting itinerary task pair;

[0115] The potential conflicting trip set V is determined by formula (4), that is, for trip tasks r and r', if the physical intervals of the operation are the same and the departure time windows overlap, it is defined as a potential conflicting trip task pair (r, r') and is put into the set V;

[0116]

[0117] In the above formula, the set T r and T r’ represents the departure timestamp set corresponding to the itinerary tasks r and r', the set V represents the set of potential conflicting itineraries, and the set R T represents a set of travel tasks; parameters a(r) and a(r') represent the running intervals corresponding to travel tasks r and r'; the "task r" field is the index used to retrieve travel task r, the "task r'" field is the index used to retrieve task r', the "timestamp t" field is the index used to retrieve timestamp t, and the "timestamp t'" field is the index used to retrieve timestamp t. The tuple (r, r') represents a potentially conflicting travel task pair;

[0118] The minimum trip frequency constraint of the Benders main problem is that for each physical operation interval and a given scenario, according to the spatiotemporal passenger flow demand information, the number of trips departing within the time window of a given scenario must not be less than the minimum number of trips, as shown in formula (33):

[0119]

[0120] In the above formula, set A represents the set of physical intervals; set S a represents the set of travel frequency requirement scenarios for physical interval a; set T s Represents the travel frequency requirement timestamp set corresponding to scenario s, set Represents the set of restricted feasible paths for train units; parameter β p,a,t Indicates whether path p passes through physical interval a at timestamp t. If path p passes through physical interval a at timestamp t, then β p,a,t =1, otherwise β p,a,t =0; parameter Represents the minimum number of trips departing within the time window corresponding to scenario s; decision variable λ p Indicates whether path p is selected. If path p is selected, then λp =1, otherwise λ p = 0; the "path p" field is an index for retrieving path p, the "interval a" field is an index for retrieving physical interval a, the "scene s" field is an index for retrieving scene s, the "task r" field is an index for retrieving trip r, and the "timestamp t" field is an index for retrieving timestamp t.

[0121] The Benders main problem itinerary coverage constraint condition is based on the flexible marshaling train operation condition requirements. For each physical operation interval and timestamp, the number of covered train units shall not exceed the train marshaling upper limit, as shown in formula (34):

[0122]

[0123] In the above formula, set A represents the physical interval set, set T represents the total planning timestamp set, and set Represents the set of restricted feasible paths for train units; parameter β p,a,t Indicates whether path p passes through physical interval a at timestamp t. If path p passes through physical interval a at timestamp t, then β p,a,t =1, otherwise β p,a,t =0; parameter represents the maximum number of train formations in interval a at any time; decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p =0; the "path p" field is an index for retrieving path p, the "interval a" field is an index for retrieving physical interval a, the "task r" field is an index for retrieving task r, and the "timestamp t" field is an index for retrieving timestamp t;

[0124] The Benders optimal cut constraint condition is constructed based on the solution of the Benders subproblem to construct the optimal cut constraint condition for the Benders main problem, as shown in formula (35):

[0125]

[0126] In the above formula, the set R T Represents the set of itinerary tasks, set T r Represents the departure timestamp set corresponding to the trip task r, the set Represents the set of restricted feasible paths for train units, the set Represents the set of restricted feasible paths for crew members; tuple (θ 1 ,θ 2 ) represents the set of extreme points in the dual space of the Benders subproblem O △The pole of p,r,t represents whether path p includes the travel task r starting at timestamp t. If path p includes the travel task r starting at timestamp t, then α p,r,t =1, otherwise α p,r,t =0; parameter represents the value of the solution of the Benders dual subproblem at the trip task r and time t; the parameter represents the value of the solution to the Benders dual subproblem at the extreme point on path p; the decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p = 0; the "path p" field is an index for retrieving path p, the "task r" field is an index for retrieving task r, and the "timestamp t" field is an index for retrieving timestamp t;

[0127] The Benders subproblem specifically includes a Benders subproblem objective function and coupling constraints between the Benders subproblem train unit and the crew;

[0128] The objective function of the Benders subproblem includes the path costs of all crew members, as shown in formula (36):

[0129]

[0130] In the above formula, the set Represents the set of restricted feasible paths for crew members; parameter C p C represents the cost of crew member path p; decision variable μ p Indicates whether path p is selected. If path p is selected, μ p =1, otherwise μ p = 0; the optimization goal min is to minimize the path costs of all crew members; the "path p" field is an index for retrieving path p;

[0131] The coupling constraint between the train unit and the crew of the Benders subproblem is that for each trip and any timestamp in its departure time range, if the trip departs, it should be guaranteed that there is a crew member assigned to the trip, as shown in formula (37):

[0132]

[0133] In the above formula, the set R T Represents the set of itinerary tasks, set T r Represents the departure timestamp set corresponding to the trip task r, the set Represents the set of restricted feasible paths for train units, the set represents the set of restricted feasible paths for crew members; parameter α p,r,t represents whether path p includes the travel task r starting at timestamp t. If path p includes the travel task r starting at timestamp t, then α p,r,t =1, otherwise α p,r,t =0; parameter Indicates whether path p is selected. If path p is selected, on the contrary Parameter γ p,r Indicates whether path p includes itinerary task r. If path p includes itinerary task r, then γ p,r =1, otherwise γ p,r =0; decision variable μ p Indicates whether path p is selected. If path p is selected, μ p =1, otherwise μ p = 0; the "path p" field is an index for retrieving path p, the "task r" field is an index for retrieving task r, and the "timestamp t" field is an index for retrieving timestamp t;

[0134] Based on the above scheme, in step 6, the pricing sub-problems are constructed for the Benders main problem and Benders sub-problem obtained in step 5, respectively, including:

[0135] The objective function of the pricing subproblem corresponding to the Benders main problem is: for the kth train unit belonging to the train unit set K and the train operation plan L k The pth path in the lth train operation plan is as shown in formula (38):

[0136]

[0137] In the above formula, set T represents the total planning timestamp set, set V represents the potential conflicting itinerary set (the set is determined by formula 32), set A represents the physical interval set, and set S a Represents the set of travel frequency requirement scenarios for physical interval a, set T s Represents the travel frequency requirement timestamp set corresponding to scenario s, set T r Represents the departure timestamp set corresponding to the trip task r, the set represents the set of restricted feasible paths corresponding to the train operation plan l, set K represents the train unit set, set L k represents the set of train operation alternatives corresponding to train unit k, set R l Trepresents the set of itinerary tasks corresponding to the operation plan l; the tuple (θ1, θ2) represents the set of extreme points in the dual space of the Benders subproblem O △ The extreme point of the set T r Represents the departure timestamp set corresponding to the trip task r, set T s Represents the timestamp set corresponding to scene s; parameter C p R represents the cost of the train unit path p; parameter represents the value of the solution of the Benders dual subproblem at the trip task r and time t; the parameter and are the dual variable values ​​corresponding to the Benders master problem constraint formulas (30), (31), (33), (34) and (35); the parameters represents the minimum number of trips departing within the time window corresponding to scenario s; parameter represents the maximum number of train formations in interval a at any time; parameter T r R represents the travel time of trip task r; decision variable α p,r,t represents whether path p includes the travel task r starting at timestamp t. If path p includes the travel task r starting at timestamp t, then α p,r,t =1, otherwise α p,r,t =0; decision variable β p,a,t Indicates whether path p passes through physical interval a at timestamp t. If path p passes through physical interval a at timestamp t, then β p,a,t =1, otherwise β p,a,t =0; the "path p" field is an index for retrieving path p, the "train unit k" field is an index for retrieving train unit k, the "running plan l" is an index for retrieving running plan l, the "task r" field is an index for retrieving task r, the "timestamp t" field is an index for retrieving timestamp t, the "timestamp t'" field is an index for retrieving timestamp t', the "interval a" field is an index for retrieving physical interval a, and the "scene s" is an index for retrieving scene s;

[0138] The objective function of the pricing subproblem corresponding to the Benders subproblem is, for each crew group, as shown in formula (39):

[0139]

[0140] In the above formula, the set represents the set of itinerary tasks of crew g, set T r Represents the departure timestamp set corresponding to the trip task r, the set It indicates the set of feasible paths corresponding to crew group g, and set G represents the crew group set; parameter represents the cost of the pth path belonging to crew g; parameter Represents the dual variable value of Formula 37; decision variable γ p,r Indicates whether path p includes itinerary task r. If path p includes itinerary task r, then γ p,r =1, otherwise γ p,r = 0; the "path p" field is an index for retrieving path p, the "path p" field is an index for retrieving path p, the "task r" field is an index for retrieving task r, and the "crew g" field is an index for retrieving crew g;

[0141] Based on the above solution, the branch-price-cut algorithm described in step 6 specifically includes:

[0142] Step 6.1: Reconstruct the train operation and crew planning collaborative optimization model M1 based on the spatiotemporal network to obtain the equivalent collaborative optimization model M2 based on the train and crew paths;

[0143] Step 6.2: According to the Benders decomposition algorithm, the linear relaxation model of model M2 is decomposed to obtain the Benders main problem model M3 and the Benders sub-problem model M4;

[0144] Step 6.3: Based on the initial train alternative path set and the crew alternative path set, use the column generation method to solve the linear relaxation model of Benders main problem M3 and Benders subproblem M4 to obtain the dual variable values ​​corresponding to each constraint condition;

[0145] Step 6.4: Based on the dual variables obtained in step 6.3, construct the pricing subproblem SPR for each train unit k and train operation plan l based on the Benders master problem M3 k,l , and further solve the pricing subproblem SPR through the label update algorithm k,l , and obtain a new train alternative route; based on the Benders subproblem M4, for each crew group g, solve the pricing subproblem SPC through the label update algorithm g , and then get a new crew alternative path; if all pricing subproblems SPR k,l and SPC g If the objective function values ​​of are all greater than or equal to zero, the current solution is proved to be the optimal solution; otherwise, repeat step 7.3 based on the newly obtained set of train or crew alternative paths to continue iterating until the pricing subproblem SPR k,l and SPC g Until the objective function values ​​of are all non-negative;

[0146] Step 6.5: The branch-price-cut algorithm includes a branching strategy, a pricing strategy and a cutting strategy;

[0147] The branching strategy includes: based on the solutions obtained from the Benders main problem and the Benders subproblems and If the corresponding values ​​are all integers, the optimal solution to the original problem is obtained. Otherwise, the decision variable closest to 0.5 is selected and fixed to 0 or 1, creating two decision branches, each of which inherits the original restrictive main problem model and the corresponding fixed variable value;

[0148] The pricing strategy includes: solving the pricing sub-problem SPR k,l and SPC g and the bounding process. For the bounding process, if the current restrictive master problem model is infeasible, or the objective function value is greater than the global upper bound value, or a feasible integer optimal solution is obtained, the node will not be branched to subsequent nodes;

[0149] The cutting strategy includes: constructing the optimal cutting constraint condition based on formula 35 according to the optimal value of the solved Benders subproblem M4 and the dual variable values ​​corresponding to each constraint condition and adding it to the Benders main problem M3.

[0150] The method for collaboratively optimizing the operation and crew planning of urban rail transit network trains described in the present invention has the following beneficial effects:

[0151] The present invention is based on the space-time network model, constructs the space-time network of train operation and crew plan, adopts the branch-pricing-cutting algorithm framework, and proposes a method for collaborative optimization of train operation and crew plan in urban rail transit network. The present invention improves the existing problem of too small adjustment space for crew plan and multiple feedback adjustments to train operation plan caused by the phased preparation of train operation and crew plan. In addition, it is worth noting that the branch-pricing-cutting algorithm method based on the space-time network model proposed in the present invention can solve the accurate optimal solution and give the upper and lower boundary convergence curves in a calculation time shorter than that of the integer programming solving software. The method proposed in the present invention can be extended to more traffic space-time path coupling optimization problems, and fully tap the redundant transportation capacity generated by the preparation of different plans. It is of great significance to improve the current rail transit network operation efficiency, passenger service level, and cost reduction and efficiency improvement of operating enterprises. BRIEF DESCRIPTION OF THE DRAWINGS

[0152] The present invention has the following accompanying drawings:

[0153] Figure 1 It is a diagram of the decision-making process of urban rail transit operation plan;

[0154] Figure 2It is the physical network and train operation plan diagram of urban rail transit;

[0155] Figure 3 It is a schematic diagram of the space-time network of the train operation process;

[0156] Figure 4 It is a Gantt chart diagram of train operation and crew planning;

[0157] Figure 5 It is a branch-price-cut algorithm framework;

[0158] Figure 6 It is a test example urban rail transit physical network diagram. DETAILED DESCRIPTION

[0159] The following is combined with Figure 5 It should be emphasized that the following description is only exemplary and is not intended to limit the scope of the present invention and its application.

[0160] The present invention proposes a new method for coordinating and optimizing the operation and crew planning of urban rail network transportation trains by analyzing the coupling relationship between train operation and crew planning under the network operation conditions of urban rail transportation. The specific implementation method of the invented method is described in detail below.

[0161] Step 1: Determine the following necessary parameters and data in advance:

[0162] (1) Physical network of urban rail transit, including depot nodes, station nodes, and section connection arcs;

[0163] (2) Train operation plan, including train starting and ending points, train operation routes, stop plans, etc.;

[0164] (3) Basic parameters of train operation, including the interval time, stop time, and travel time of various trains;

[0165] (4) Basic parameters of crew members, including the number of crew members, the number of available crew members for each crew member, and the available working hours for each crew member;

[0166] Step 2: Given the above conditions, write code in C++ or Python to build the model framework proposed by this method and obtain the corresponding train operation and crew plan.

[0167] Step 3: The results can be adjusted to a certain extent according to the actual situation.

[0168] Example 1

[0169] like Figure 6The urban rail transit network shown contains 3 physical sections, 4 stations, and 2 yards. The train has 3 alternative train operation plans, and the following known conditions are given:

[0170] (1) Physical network of urban rail transit. Consider a “Y-shaped” bidirectional urban rail network, such as Figure 6 As shown in (a), the network contains 3 physical sections, 4 stations, and 2 yards. For ease of description, the stations are named S1 to S4, and the three yards D1, D2, and D3 are connected to S1, S3, and S4 stations respectively. According to the needs of passenger flow, this example considers 2 to 5 available train units, 2 to 8 train operation plans, and 8 to 26 train trips in different test experiments.

[0171] (2) Consider one crew that can be on duty on any train journey within the entire time range. The crew can have a maximum of 26 crew members.

[0172] (3) The planning time domain is set to 0 min-60 min, with 1 min as the discrete time granularity, and includes a total of 60 time nodes.

[0173] (4) Basic parameters and costs of train operation are shown in Table 1.

[0174] Table 1

[0175]

[0176] In this embodiment, since there are relatively few variables and constraints involved, the CPLEX solver and the proposed algorithm are used simultaneously to solve the proposed problem and mathematical model. To meet the real-time requirements, the following solution termination conditions are set: (a) When the CPLEX solver finds a feasible solution with a relative gap of 0%, the solution stops; (b) To meet the real-time requirements, when the solution time exceeds 300s, the search process can be terminated. Specifically, the solution results and related performance of four groups of examples of different sizes tested using CPLEX and the branch-price-cut algorithm are shown in Table 2.

[0177] From the statistical results, it can be seen that the method proposed in this patent has achieved better performance in all four examples. Among them, in Example 1, Example 2 and Example 3, the method proposed in this patent can find the optimal solution in a shorter running time (relative gap is 0.000%) compared with the CPLEX solver; in Example 4, the method proposed in this patent can find an optimal solution with a lower relative gap of only 2.509% in the same 300.000s running time compared with the CPLEX solver. In terms of average performance, compared with the CPLEX solver, the method proposed in this patent can reduce the average relative gap by 66% and the average calculation time by 33% under the same conditions.

[0178] Table 2

[0179]

[0180] In summary, the present invention uses the modeling concept of system optimization to propose a new collaborative optimization method for urban rail transit network train operation and crew use. This method can effectively balance the problem scale and efficiency of Benders decomposition and column generation algorithm to solve collaborative optimization, greatly improve the quality of accurate solutions and reduce solution calculation time, and effectively improve the shortcomings of traditional methods.

[0181] It should be noted that the above is only a specific implementation of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the art can easily modify and transform the proposed model within the technical scope of the present invention, and these modifications or replacements do not make the essence of the corresponding technical solution deviate from the spirit and scope of each implementation of the technical solution of the present invention. The protection scope of the present invention is limited only by the attached claims.

[0182] The contents not described in detail in this specification belong to the prior art known to professional and technical personnel in this field.

Claims

1. A method for collaborative optimization of train operation and crew planning in an urban rail transit network, characterized in that: The steps include: Step 1: Based on the discrete space-time network, describe the process of train units entering and leaving the yard, marshaling, disassembling and turning back, as well as the crew's duty, dining and resting processes; Step 2: Construct train operation organization constraints and crew scheduling constraints; The train operation organization constraints include: train operation plan selection constraints, trip departure time constraints, train safety interval constraints, minimum trip frequency constraints, trip coverage constraints, train unit return constraints, and train connection time constraints; Crew scheduling constraints include: crew task allocation constraints, crew task flow balance constraints, crew meal / rest task quantity balance constraints, crew on-duty and off-duty balance constraints, task connection time constraints, crew meal / rest frequency constraints, crew meal / rest time window constraints, train itinerary and crew task coupling constraints, and crew quantity constraints; Step 3: Based on the train operation organization constraints and crew scheduling constraints described in step 2, a collaborative optimization model is constructed with the minimum total train operation cost and crew scheduling cost as the objective function; The total train operation cost includes the fixed cost of train operation plan, fixed cost of trip and trip connection cost; The crew scheduling cost includes the fixed cost of crew number; Step 4: Based on the collaborative optimization model of train operation and crew planning constructed in step 3, reconstruct an equivalent collaborative optimization model based on train and crew paths; Step 5: Construct the Benders main problem and Benders sub-problem for the equivalent collaborative optimization model based on the train and crew paths obtained in step 4; Step 6: For the Benders main problem and Benders subproblem obtained in step 5, construct pricing subproblems respectively, and design a branch-price-cut algorithm to solve them until a feasible and better collaborative optimization solution is obtained.

2. A method for collaborative optimization of train operation and crew planning in an urban rail transit network as claimed in claim 1, characterized in that: Step 1 specifically includes: For the train operation organization process, according to the accuracy requirements, the train planning time domain is discretized into a set of timestamps to form a timestamp set; According to the discrete timestamp set, all physical nodes in the urban rail transit network are expanded in time and space; the physical nodes after time and space expansion include the time and space nodes of the station, the starting point of the yard and the end point of the yard; Based on the above-mentioned space-time node set, a corresponding space-time arc set is constructed; specifically, it includes train travel arcs, entry / exit yard arcs, and connection arcs; For the crew's duty process, a crew dining task set is constructed to describe the crew's dining behavior; a crew rest task set is constructed to describe the crew's rest behavior.

3. The method for collaborative optimization of train operation and crew planning in an urban rail transit network according to claim 1, characterized in that: The train operation organization constraints described in step 2 specifically include: The train operation plan selection constraint condition is: for each train unit, only one suitable train operation plan can be selected from its corresponding train operation plan alternative set, as shown in formula (1): In the above formula, set K represents the train unit set, set L k represents the set of alternative train operation plans corresponding to train unit k; decision variable u k,l Indicates whether the train operation plan l is selected by the train unit k. If the train operation plan l is selected by the train unit k, then u k,l =1, otherwise u k,l =0; The trip departure time constraint condition is used to ensure that each trip in the train operation plan selected by the train unit departs within its specified time window, as shown in formula (2): In the above formula, set K represents the train unit set, set L k represents the set of train operation alternatives corresponding to train unit k, set R l T represents the set of itinerary tasks corresponding to the operation plan l; set T r represents the departure timestamp set corresponding to the trip task r; the decision variable x r,t represents whether the trip task r departs at timestamp t. If the trip task r departs at timestamp t, then x r,t =1, otherwise x r,t =0; decision variable u k,l Indicates whether the train operation plan l is selected by the train unit k. If the train operation plan l is selected by the train unit k, then u k,l =1, otherwise u k,l =0; The train safety interval constraint condition is used to ensure that there is no conflict between the trips to ensure the safe operation of the train, as shown in formula (3): In the above formula, set T represents the total planning timestamp set, set T r and T r’ represents the departure timestamp set corresponding to the itinerary tasks r and r', and the set V represents the set of potential conflicting itineraries; the parameters represents the minimum safe interval between potentially conflicting tasks r and r'; decision variable x r,t represents whether the trip task r departs at timestamp t. If the trip task r departs at timestamp t, then x r,t =1, otherwise x r,t =0; The potential conflicting trip set V is determined by formula (4), that is, for trip tasks r and r', if the physical intervals of the operation are the same and the departure time windows overlap, it is defined as a potential conflicting trip task pair (r, r') and is put into the set V; In the above formula, the set T r and T r’ represents the departure timestamp set corresponding to the itinerary tasks r and r', the set V represents the set of potential conflicting itineraries, and the set R T represents a set of travel tasks; parameters a(r) and a(r') represent the operating intervals corresponding to travel tasks r and r'; The minimum trip frequency constraint condition is that for each physical operation interval and a given scenario, according to the spatiotemporal passenger flow demand information, the number of trips departing within the time window of a given scenario must not be less than the minimum number of trips, as shown in formula (5): In the above formula, set A represents the set of physical intervals; set S a represents the set of travel frequency requirement scenarios for physical interval a; set T s represents the travel frequency requirement timestamp set corresponding to scenario s; set T r Represents the departure timestamp set corresponding to the trip task r; set R T Represents a set of itinerary tasks; parameters Represents the minimum number of trips departing from the timestamp set corresponding to scenario s; parameter δ r,a Indicates whether the trip task r passes through the physical interval a. If the trip task r passes through interval a, then δ r,a =1, otherwise δ r,a =0; decision variable x r,t represents whether the trip task r departs at timestamp t. If the trip task r departs at timestamp t, then x r,t =1, otherwise x r,t =0; The trip coverage constraint condition is based on the flexible marshaling train operation condition requirements. For each physical operation interval and timestamp, the number of covered train units shall not exceed the train marshaling upper limit, as shown in formula (6): In the above formula, set A represents the physical interval set, set T represents the total planning timestamp set, and set R T represents the set of itinerary tasks; parameter δ r,a Indicates whether the trip task r passes through the physical interval a. If the trip task r passes through interval a, then δ r,a =1, otherwise δ r,a =0; parameter represents the maximum number of train formations in interval a at any time; decision variable x r,t represents whether the trip task r departs at timestamp t. If the trip task r departs at timestamp t, then x r,t =1, otherwise x r,t =0; The train unit reversal constraint condition is used to ensure that the connection time of the train unit when connecting two adjacent trips shall not be less than the minimum reversal time and shall not exceed the maximum reversal time, as shown in formulas (7) and (8): In the above two equations, set K represents the train unit set, and set L k represents the set of train operation alternatives corresponding to train unit k, set R l T represents the set of itinerary tasks corresponding to the operation plan l; set T r and T σ(r) represents the departure timestamp set corresponding to the trip task r and σ(r); parameter r0(l) represents the first trip task r0(l) of the train operation plan l, parameter represents the travel time of the trip task σ(r); parameter represents the minimum connection time between the trip task σ(r) and the trip task r; parameter represents the maximum connection time between the trip task σ(r) and the trip task r; the decision variable x r,t represents whether the trip task r departs at timestamp t. If the trip task r departs at timestamp t, then x r,t =1, otherwise x r,t =0; decision variable u k,l Indicates whether the train operation plan l is selected by the train unit k. If the train operation plan l is selected by the train unit k, then u k,l =1, otherwise u k,l =0; The train connection time constraint is used to calculate the actual return time of the train unit between two adjacent trips, as shown in formula (9): In the above formula, set K represents the train unit set, set L k represents the set of train operation alternatives corresponding to train unit k, set R l T represents the set of itinerary tasks corresponding to the operation plan l; set T r and T σ(r) represents the departure timestamp set corresponding to the trip task r and σ(r); the parameter σ(r) represents the only previous trip task of the trip task r, and the parameter r0(l) represents the first trip task of the train operation plan l; the parameter represents the travel time of the trip task σ(r); the decision variable x r,t represents whether the trip task r departs at timestamp t. If the trip task r departs at timestamp t, then x r,t =1, otherwise x r,t =0; decision variable v k,σ(r),r Represents the actual connection time between train unit k and trip tasks σ(r) and r.

4. The method for collaborative optimization of train operation and crew planning in an urban rail transit network according to claim 1, characterized in that: The crew scheduling constraints described in step 2 specifically include: The crew task allocation constraint condition is that for each crew member, at most one trip or meal / rest task starts, as shown in formula (10): In the above formula, set C represents the crew set; set R T Represents the set of itinerary tasks, set R c M represents the dining task set corresponding to crew member c, set R c R represents the rest task set corresponding to crew member c; decision variable z c,0,r Indicates whether the trip task r is connected to the virtual starting node. If the trip task r is connected to the virtual starting node, then z c,0,r =1, otherwise z c,0,r =0; The flow balance constraint of the crew tasks is that for each crew member, any trip or meal / rest task needs to be connected to other tasks or start / end nodes, as shown in formula (11): In the above formula, set C represents the crew set; set R T Represents the set of itinerary tasks, set R c M represents the dining task set corresponding to crew member c, set R c R represents the set of rest tasks corresponding to crew member c; set R r T- Represents the set of previous consecutive trip tasks of trip task r, set R r T+ represents the set of next consecutive trip tasks of trip task r; decision variable z c,0,r Indicates whether the trip task r is connected to the virtual starting node. If the trip task r is connected to the virtual starting node, then z c,0,r =1, otherwise z c,0,r =0; decision variable z c,r’,r Indicates whether the trip task r is connected to another trip task r'. If the trip task r is connected to another trip task r', then z c,r’,r =1, otherwise z c,r’,r =0; decision variable z c,r,0 Indicates whether the trip task r is connected to the virtual destination node. If the trip task r is connected to the virtual destination node, then z c,r,0 =1; otherwise z c,r,0 =0; The balance constraint of the number of crew members' dining tasks and rest tasks is that for each crew member's dining task and rest task, there can only be two trip tasks as its next and previous successor tasks, as shown in formula (12): In the above formula, set C represents the crew set; set R c M represents the dining task set corresponding to crew member c, set R c R represents the rest task set corresponding to crew member c; set R r T- Represents the set of previous consecutive trip tasks of trip task r, set R r T+ represents the set of next consecutive trip tasks of trip task r; decision variable z c,0,r Indicates whether the trip task r is connected to the virtual starting node. If the trip task r is connected to the virtual starting node, then z c,0,r =1, otherwise z c,0,r =0; decision variable z c,r’,r Indicates whether the trip task r is connected to another trip task r'. If the trip task r is connected to another trip task r', then z c,r’,r =1, otherwise z c,r’,r =0; decision variable z c,r,0 Indicates whether the trip task r is connected to the virtual destination node. If the trip task r is connected to the virtual destination node, then z c,r,0 =1; otherwise z c,r,0 =0; The crew on-duty and off-duty balance constraint ensures that there is a first and last task for each crew member on duty, and that there is no first and last task for each crew member not on duty, as shown in formula (13): In the above formula, set C represents the crew set, set R T Represents the set of itinerary tasks, set R c M represents the dining task set corresponding to crew member c, set R c R represents the rest task set corresponding to crew member c; decision variable z c,0,r Indicates whether the trip task r is connected to the virtual starting node. If the trip task r is connected to the virtual starting node, then z c,0,r =1, otherwise z c,0,r =0; decision variable z c,r,0 Indicates whether the trip task r is connected to the virtual destination node. If the trip task r is connected to the virtual destination node, then z c,r,0 =1; otherwise z c,r,0 =0; The task connection time constraint is used to ensure that the connection time between two consecutive tasks performed by the crew members meets the specified requirements, as shown in formulas (14) and (15): In the above two equations, set C represents the crew set, set R T Represents the set of itinerary tasks, set R c M represents the dining task set corresponding to crew member c, set R c R represents the rest task set corresponding to crew member c; set T r and T r ' represents the departure timestamp set corresponding to the trip tasks r and r'; parameter and Respectively represent the minimum and maximum connection time between two consecutive tasks performed by the crew; parameter T r R represents the travel time of trip task r; the decision variable x r,t represents whether the trip task r departs at timestamp t. If the trip task r departs at timestamp t, then x r,t =1, otherwise x r,t =0; decision variable z c,r,r’ Indicates whether the trip task r' is connected to another trip task r. If the trip task r' is connected to another trip task r, then z c,r,r’ =1, otherwise z c,r,r’ =0; parameter M r,r’ represents the maximum M value corresponding to r and r' in formula (14) and formula (15), which is determined by formula (16): In the above formula, set C represents the crew set, set R T Represents the set of itinerary tasks, set R c M represents the dining task set corresponding to crew member c, set R c R represents the rest task set corresponding to crew member c; parameter T r and Respectively represent the earliest start time and the latest start time of the trip task r; parameter T r R represents the travel time of trip task r; parameter It represents the maximum connection time between two consecutive tasks performed by crew members; The crew meal / rest frequency constraint ensures that every crew member on duty must perform the corresponding meal / rest task, as shown in formula (17): In the above formula, set C represents the crew set, set R T Represents the set of itinerary tasks, set R c M represents the dining task set corresponding to crew member c, set R c R represents the rest task set corresponding to crew member c, set R r T- represents the set of previous consecutive trip tasks of trip task r; decision variable z c,0,r Indicates whether the trip task r is connected to the virtual starting node. If the trip task r is connected to the virtual starting node, then z c,0,r =1, otherwise z c,0,r =0; decision variable z c,r’,r Indicates whether the trip task r is connected to another trip task r'. If the trip task r is connected to another trip task r', then z c,r’,r =1, otherwise z c,r’,r =0; The crew meal / rest time window constraint ensures that each meal / rest task must be executed within the specified time window, as shown in formula (18): Among them, set C represents the crew set, set R T Represents the set of itinerary tasks, set R c M represents the dining task set corresponding to crew member c, set R c R represents the rest task set corresponding to crew member c, set T r represents the departure timestamp set corresponding to the trip task r; the decision variable x r,t represents whether the trip task r departs at timestamp t. If the trip task r departs at timestamp t, then x r,t =1, otherwise x r,t =0; decision variable z c,0,r Indicates whether the trip task r is connected to the virtual starting node. If the trip task r is connected to the virtual starting node, then z c,0,r =1, otherwise z c,0,r =0; decision variable z c,r’,r Indicates whether the trip task r is connected to another trip task r'. If the trip task r is connected to another trip task r', then z c,r’,r =1, otherwise z c,r’,r =0; The train itinerary and crew task coupling constraint, for any itinerary, should ensure that at least one crew member is assigned to the itinerary, as shown in formula (19): Among them, set C represents the crew set, set R T Represents the set of itinerary tasks, set R c M represents the dining task set corresponding to crew member c, set R c R represents the rest task set corresponding to crew member c, set T r Represents the departure timestamp set corresponding to the trip task r, set R r T - represents the previous set of tasks that follow the trip task r; decision variable x r,t represents whether the trip task r departs at timestamp t. If the trip task r departs at timestamp t, then x r,t =1, otherwise x r,t =0; decision variable z c,0,r Indicates whether the trip task r is connected to the virtual starting node. If the trip task r is connected to the virtual starting node, then z c,0,r =1, otherwise z c,0,r =0; decision variable z c,r’,r Indicates whether the trip task r is connected to another trip task r'. If the trip task r is connected to another trip task r', then z c,r’,r =1, otherwise z c,r’,r =0; The crew number constraint is used to calculate the number of crew members actually used for work by each crew group, as shown in formula (20): Among them, set G represents the crew set, set C g represents the crew set corresponding to crew group g, set R T Represents the set of itinerary tasks, set R c M represents the dining task set corresponding to crew member c, set R c R represents the rest task set corresponding to crew member c; decision variable m g represents the number of crew members corresponding to crew group g; decision variable z c,0,r Indicates whether the trip task r is connected to the virtual starting node. If the trip task r is connected to the virtual starting node, then z c,0,r =1, otherwise z c,0,r =0.

5. The method for collaborative optimization of train operation and crew planning in urban rail transit network according to claim 1, characterized in that: The objective function described in step 3 is to minimize the total train operating cost and crew scheduling cost, as shown in formula (21): The first item is the sum of fixed costs of the train operation plan, the second item is the sum of train travel costs, the third item is the sum of train unit connection costs, and the fourth item is the sum of crew costs; Set K represents the train unit set, set L k represents the set of train operation alternatives corresponding to train unit k, set R l T represents the set of itinerary tasks corresponding to the operation plan l; set T r represents the departure timestamp set corresponding to the trip task r, and the set G represents the crew set; the optimization goal min is to minimize the total cost; the decision variable u k,l Indicates whether the train operation plan l is selected by the train unit k. If the train operation plan l is selected by the train unit k, then u k,l =1, otherwise u k,l =0; decision variable x r,t represents whether the trip task r departs at timestamp t. If the trip task r departs at timestamp t, then x r,t =1, otherwise x r,t =0; decision variable v k,σ(r),r represents the actual connection time between train unit k and trip tasks σ(r) and r; Decision variable m g Represents the number of crew members corresponding to crew group g; parameter c k,l 1 represents the fixed cost of train unit k choosing train operation plan l; parameter c r,t 2 represents the fixed cost of the trip task r starting at timestamp t; parameter c σ(r),r 3 represents the fixed cost per unit time of the trip task σ(r) and the trip task r; parameter c g 4 represents the fixed cost of arranging a crew member in crew group g, parameter r0(l) represents the first trip task of train operation plan l, and parameter σ(r) represents the only previous trip task of trip task r.

6. A method for collaborative optimization of train operation and crew planning in an urban rail transit network as claimed in claim 1, characterized in that: The train operation and crew planning collaborative optimization model constructed based on step 3 described in step 4 is reconstructed to obtain a collaborative optimization model based on train and crew paths, which specifically includes: The collaborative optimization model based on the train and crew paths specifically includes train unit path selection constraints, train safety interval constraints based on the train path, minimum travel frequency constraints based on the train path, travel coverage constraints based on the train path, and coupling constraints between train units and crew based on the train path; The train unit path selection constraint condition is that for each train unit, only one path can be selected from its feasible path set, as shown in formula (22): In the above formula, the set represents the set of feasible paths corresponding to train unit k, where set K represents the set of train units; decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p =0; The train safety interval constraint condition based on the train path ensures that there is no conflict between the trips to ensure the safe operation of the train, as shown in formula (23): In the above formula, set T represents the total planning timestamp set, set V represents the potential conflicting itinerary set, and set P R Represents the set of feasible paths for the train unit; parameter Represents the minimum safe interval between potentially conflicting itinerary tasks r and r'; parameter α p,r,t represents whether path p includes the travel task r starting at timestamp t. If path p includes the travel task r starting at timestamp t, then α p,r,t =1, otherwise α p,r,t =0; decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p =0; The potential conflicting trip set V is determined by formula (4), that is, for trip tasks r and r', if the physical intervals of the operation are the same and the departure time windows overlap, it is defined as a potential conflicting trip task pair (r, r') and is put into the set V; In the above formula, the set T r and T r’ represents the departure timestamp set corresponding to the itinerary tasks r and r', the set V represents the set of potential conflicting itineraries, and the set R T represents a set of travel tasks; parameters a(r) and a(r') represent the operating intervals corresponding to travel tasks r and r'; The minimum trip frequency constraint condition based on the train path is that for each physical operation interval and a given scenario, according to the spatiotemporal passenger flow demand information, the number of trips departing within the time window of a given scenario shall not be less than the minimum number of trips, as shown in formula (25): In the above formula, set A represents the set of physical intervals; set S a represents the set of travel frequency requirement scenarios for physical interval a; set T s represents the set of travel frequency requirements timestamps corresponding to scenario s, set P R represents the set of feasible paths for the train unit; parameter β p,a,t Indicates whether path p passes through physical interval a at timestamp t. If path p passes through physical interval a at timestamp t, then β p,a,t =1, otherwise β p,a,t =0; parameter Represents the minimum number of trips departing within the time window corresponding to scenario s; decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p =0; The travel coverage constraint condition based on the train path is based on the flexible marshaling train operation condition requirements. For each physical operation interval and timestamp, the number of covered train units shall not exceed the train marshaling upper limit, as shown in formula (26): In the above formula, set A represents the physical interval set, set T represents the total planning timestamp set, and set P R represents the set of feasible paths for the train unit; parameter β p,a,t Indicates whether path p passes through physical interval a at timestamp t. If path p passes through physical interval a at timestamp t, then β p,a,t =1, otherwise β p,a,t =0; parameter represents the maximum number of train formations in interval a at any time; decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p =0; The coupling constraint between the train unit and the crew is that for each trip and any timestamp in its departure time range, if the trip departs, it should be guaranteed that a crew member is assigned to the trip, as shown in formula (27): In the above formula, the set R T Represents the set of itinerary tasks, set T r represents the departure timestamp set corresponding to the trip task r, set P R represents the set of feasible paths for train units, set P C represents the set of feasible paths for crew members; parameter α p,r,t represents whether path p includes the travel task r starting at timestamp t. If path p includes the travel task r starting at timestamp t, then α p,r,t =1, otherwise α p,r,t =0; parameter γ p,r Indicates whether path p includes itinerary task r. If path p includes itinerary task r, then γ p,r =1, otherwise γ p,r =0; decision variable μ p Indicates whether path p is selected. If path p is selected, μ p =1, otherwise μ p =0; decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p =0; The objective function is to minimize the total train operating cost and crew scheduling cost, as shown in formula (28): In the above formula, the set P R represents the set of feasible paths for train units, set P C represents the set of feasible paths for crew members; parameter C p R represents the cost of the train unit path p, parameter C p C represents the cost of crew member path p; decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p =0; decision variable μ p Indicates whether path p is selected. If path p is selected, μ p =1, otherwise μ p =0.

7. A method for collaborative optimization of train operation and crew planning in an urban rail transit network as claimed in claim 1, characterized in that: The train operation and crew planning collaborative optimization model based on the spatiotemporal network described in step 5 constructs the Benders main problem and Benders sub-problems, which specifically include: The Benders main problem specifically includes the Benders main problem objective function, the Benders main problem train unit path selection constraint, the Benders main problem train safety interval constraint, the Benders main problem minimum travel frequency constraint, the Benders main problem travel coverage constraint and the Benders optimal cut constraint; The objective function of the Benders main problem includes the total train operating cost and the Benders optimal cut upper bound, as shown in formula (29): In the above formula, the set Represents the set of restricted feasible paths for train units; parameter C p R represents the cost of the train unit path p; the decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p =0; the decision variable η represents the upper limit of the Benders optimal cut; the optimization objective min is to minimize the total train operating cost and the upper limit of the Benders optimal cut; The Benders master problem train unit path selection constraint condition is that for each train unit, only one path can be selected from its restricted feasible path set, as shown in formula (30): In the above formula, the set represents the set of restricted feasible paths corresponding to train unit k, where set K represents the set of train units; decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p =0; The Benders main problem train safety interval constraint condition ensures that there is no conflict between the trips to ensure the safe operation of the train, as shown in formula (31): In the above formula, set T represents the total planning timestamp set, set T r and T r’ represents the departure timestamp set corresponding to the itinerary tasks r and r', set V represents the set of potential conflicting itineraries, and set Represents the set of restricted feasible paths for train units; parameters Represents the minimum safe interval between potentially conflicting itinerary tasks r and r'; parameter α p,r,t represents whether path p includes the travel task r starting at timestamp t. If path p includes the travel task r starting at timestamp t, then α p,r,t =1, otherwise α p,r,t =0; decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p =0; The potential conflicting trip set V is determined by formula (4), that is, for trip tasks r and r', if the physical intervals of the operation are the same and the departure time windows overlap, it is defined as a potential conflicting trip task pair (r, r') and is put into the set V; In the above formula, the set T r and T r’ represents the departure timestamp set corresponding to the itinerary tasks r and r', the set V represents the set of potential conflicting itineraries, and the set R T represents a set of travel tasks; parameters a(r) and a(r') represent the operating intervals corresponding to travel tasks r and r'; The minimum trip frequency constraint of the Benders main problem is that for each physical operation interval and a given scenario, according to the spatiotemporal passenger flow demand information, the number of trips departing within the time window of a given scenario must not be less than the minimum number of trips, as shown in formula (33): In the above formula, set A represents the set of physical intervals; set S a represents the set of travel frequency requirement scenarios for physical interval a; set T s Represents the travel frequency requirement timestamp set corresponding to scenario s, set Represents the set of restricted feasible paths for train units; parameter β p,a,t Indicates whether path p passes through physical interval a at timestamp t. If path p passes through physical interval a at timestamp t, then β p,a,t =1, otherwise β p,a,t =0; parameter Represents the minimum number of trips departing within the time window corresponding to scenario s; decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p =0; The Benders main problem itinerary coverage constraint condition is based on the flexible marshaling train operation condition requirements. For each physical operation interval and timestamp, the number of covered train units shall not exceed the train marshaling upper limit, as shown in formula (34): In the above formula, set A represents the physical interval set, set T represents the total planning timestamp set, and set Represents the set of restricted feasible paths for train units; parameter β p,a,t Indicates whether path p passes through physical interval a at timestamp t. If path p passes through physical interval a at timestamp t, then β p,a,t =1, otherwise β p,a,t =0; parameter represents the maximum number of train formations in interval a at any time; decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p =0; The Benders optimal cut constraint condition is constructed based on the solution of the Benders subproblem to construct the optimal cut constraint condition for the Benders main problem, as shown in formula (35): In the above formula, the set R T Represents the set of itinerary tasks, set T r Represents the departure timestamp set corresponding to the trip task r, the set Represents the set of restricted feasible paths for train units, the set Represents the set of restricted feasible paths for crew members; tuple (θ 1 ,θ 2 ) represents the set of extreme points in the dual space of the Benders subproblem O △ The pole of p,r,t represents whether path p includes the travel task r starting at timestamp t. If path p includes the travel task r starting at timestamp t, then α p,r,t =1, otherwise α p,r,t =0; parameter represents the value of the solution of the Benders dual subproblem at the trip task r and time t; the parameter represents the value of the solution to the Benders dual subproblem at the extreme point on path p; the decision variable λ p Indicates whether path p is selected. If path p is selected, then λ p =1, otherwise λ p =0; The Benders subproblem specifically includes a Benders subproblem objective function and coupling constraints between the Benders subproblem train unit and the crew; The objective function of the Benders subproblem includes the path costs of all crew members, as shown in formula (36): In the above formula, the set Represents the set of restricted feasible paths for crew members; parameter C p C represents the cost of crew member path p; decision variable μ p Indicates whether path p is selected. If path p is selected, μ p =1, otherwise μ p =0; the optimization goal min is to minimize the path costs of all crew members; The coupling constraint between the train unit and the crew of the Benders subproblem is that for each trip and any timestamp in its departure time range, if the trip departs, it should be guaranteed that a crew member is assigned to the trip, as shown in formula (37): In the above formula, the set R T Represents the set of itinerary tasks, set T r Represents the departure timestamp set corresponding to the trip task r, the set Represents the set of restricted feasible paths for train units, the set represents the set of restricted feasible paths for crew members; parameter α p,r,t represents whether path p includes the travel task r starting at timestamp t. If path p includes the travel task r starting at timestamp t, then α p,r,t =1, otherwise α p,r,t =0; parameter Indicates whether path p is selected. If path p is selected, on the contrary Parameter γ p,r Indicates whether path p includes itinerary task r. If path p includes itinerary task r, then γ p,r =1, otherwise γ p,r =0; decision variable μ p Indicates whether path p is selected. If path p is selected, μ p =1, otherwise μ p =0.

8. The method for collaborative optimization of train operation and crew planning in urban rail transit network according to claim 1, characterized in that: In step 6, the pricing sub-problems are constructed for the Benders main problem and the Benders sub-problem obtained in step 5, respectively, including: The objective function of the pricing subproblem corresponding to the Benders main problem is: for the kth train unit belonging to the train unit set K and the train operation plan L k The pth path in the lth train operation plan is as shown in formula (38): In the above formula, set T represents the total planning timestamp set, set V represents the potential conflicting itinerary set (the set is determined by formula 32), set A represents the physical interval set, and set S a Represents the set of travel frequency requirement scenarios for physical interval a, set T s Represents the travel frequency requirement timestamp set corresponding to scenario s, set T r Represents the departure timestamp set corresponding to the trip task r, the set represents the set of restricted feasible paths corresponding to the train operation plan l, set K represents the train unit set, set L k represents the set of train operation alternatives corresponding to train unit k, set R l T represents the set of itinerary tasks corresponding to the operation plan l; the tuple (θ1, θ2) represents the set of extreme points in the dual space of the Benders subproblem O △ The extreme point of r Represents the departure timestamp set corresponding to the trip task r, set T s Represents the timestamp set corresponding to scene s; parameter C p R represents the cost of the train unit path p; parameter represents the value of the solution of the Benders dual subproblem at the trip task r and time t; the parameter and are the dual variable values ​​corresponding to the Benders master problem constraint formulas (30), (31), (33), (34) and (35); the parameters represents the minimum number of trips departing within the time window corresponding to scenario s; parameter represents the maximum number of train formations in interval a at any time; parameter T r R represents the travel time of trip task r; decision variable α p,r,t represents whether path p includes the travel task r starting at timestamp t. If path p includes the travel task r starting at timestamp t, then α p,r,t =1, otherwise α p,r,t =0; decision variable β p,a,t Indicates whether path p passes through physical interval a at timestamp t. If path p passes through physical interval a at timestamp t, then β p,a,t =1, otherwise β p,a,t =0; The objective function of the pricing subproblem corresponding to the Benders subproblem is, for each crew group, as shown in formula (39): In the above formula, the set represents the set of itinerary tasks of crew g, set T r Represents the departure timestamp set corresponding to the trip task r, the set It indicates the set of feasible paths corresponding to crew group g, and set G represents the crew group set; parameter represents the cost of the pth path belonging to crew g; parameter Represents the dual variable value of Formula 37; decision variable γ p,r Indicates whether path p includes itinerary task r. If path p includes itinerary task r, then γ p,r =1, otherwise γ p,r =0.

9. The method for collaborative optimization of train operation and crew planning in urban rail transit network according to claim 1, characterized in that: The branch-price-cut algorithm described in step 6 specifically includes: Step 6.1: Reconstruct the train operation and crew planning collaborative optimization model M1 based on the spatiotemporal network to obtain the equivalent collaborative optimization model M2 based on the train and crew paths; Step 6.2: According to the Benders decomposition algorithm, the linear relaxation model of model M2 is decomposed to obtain the Benders main problem model M3 and the Benders sub-problem model M4; Step 6.3: Based on the initial train alternative path set and the crew alternative path set, use the column generation method to solve the linear relaxation model of Benders main problem M3 and Benders subproblem M4 to obtain the dual variable values ​​corresponding to each constraint condition; Step 6.4: Based on the dual variables obtained in step 6.3, construct the pricing subproblem SPR for each train unit k and train operation plan l based on the Benders master problem M3 k,l , and further solve the pricing subproblem SPR through the label update algorithm k,l , and obtain a new train alternative route; based on the Benders subproblem M4, for each crew group g, solve the pricing subproblem SPC through the label update algorithm g , and then get a new crew alternative path; if all pricing subproblems SPR k,l and SPC g If the objective function values ​​of are all greater than or equal to zero, the current solution is proved to be the optimal solution; otherwise, repeat step 7.3 based on the newly obtained set of train or crew alternative paths to continue iterating until the pricing subproblem SPR k,l and SPC g Until the objective function values ​​of are all non-negative; Step 6.5: The branch-price-cut algorithm includes a branching strategy, a pricing strategy and a cutting strategy; The branching strategy includes: based on the solutions obtained from the Benders main problem and the Benders subproblems and If the corresponding values ​​are all integers, the optimal solution to the original problem is obtained. Otherwise, the decision variable closest to 0.5 is selected and fixed to 0 or 1, creating two decision branches, each of which inherits the original restrictive main problem model and the corresponding fixed variable value; The pricing strategy includes: solving the pricing sub-problem SPR k,l and SPC g and the bounding process. For the bounding process, if the current restrictive master problem model is infeasible, or the objective function value is greater than the global upper bound value, or a feasible integer optimal solution is obtained, the node will not be branched to subsequent nodes; The cutting strategy includes: constructing the optimal cutting constraint condition based on formula 35 according to the optimal value of the solved Benders subproblem M4 and the dual variable values ​​corresponding to each constraint condition and adding it to the Benders main problem M3.

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